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1. Cournot competition
From Wikipedia, the free encyclopedia
Cournot competition is an economic model used to describe an industry structure in which companies compete on the amount
of output they will produce, which they decide on independently of each other and at the same time. It is named after Antoine
Augustin Cournot[1] (1801–1877) who was inspired by observing competition in a spring water duopoly. It has the following
features:
 There is more than one firm and all firms produce a homogeneous product, i.e. there is no product differentiation;
 Firms do not cooperate, i.e. there is no collusion;
 Firms have market power, i.e. each firm's output decision affects the good's price;
 The number of firms is fixed;
 Firms compete in quantities, and choose quantities simultaneously;
 The firms are economically rational and act strategically, usually seeking to maximize profit given their competitors'
decisions.
An essential assumption of this model is the "not conjecture" that each firm aims to maximize profits, based on the expectation
that its own output decision will not have an effect on the decisions of its rivals. Price is a commonly known decreasing function
of total output. All firms know , the total number of firms in the market, and take the output of the others as given. Each firm
has a cost function . Normally the cost functions are treated as common knowledge. The cost functions may be the same
or different among firms. The market price is set at a level such that demand equals the total quantity produced by all firms. Each
firm takes the quantity set by its competitors as a given, evaluates its residual demand, and then behaves as a monopoly.
]Graphically finding the Cournot duopoly equilibrium
This section presents an analysis of the model with 2 firms and constant marginal cost.
= firm 1 price, = firm 2 price
= firm 1 quantity, = firm 2 quantity
= marginal cost, identical for both firms
Equilibrium prices will be:
This implies that firm 1’s profit is given by
 Calculate firm 1’s residual demand: Suppose firm 1 believes firm 2 is producing quantity . What is
firm 1's optimal quantity? Consider the diagram 1. If firm 1 decides not to produce anything, then price
is given by . If firm 1 produces then price is given
by . More generally, for each quantity that firm 1 might decide to set, price is given

2. by the curve . The curve is called firm 1’s residual demand; it gives all possible
combinations of firm 1’s quantity and price for a given value of .
 Determine firm 1’s optimum output: To do this we must find where marginal revenue equals marginal
cost. Marginal cost (c) is assumed to be constant. Marginal revenue is a curve - - with twice
the slope of and with the same vertical intercept. The point at which the two curves (
and ) intersect corresponds to quantity . Firm 1’s optimum , depends
on what it believes firm 2 is doing. To find an equilibrium, we derive firm 1’s optimum for other
possible values of . Diagram 2 considers two possible values of . If , then the first
firm's residual demand is effectively the market demand, . The optimal solution is
for firm 1 to choose the monopoly quantity; ( is monopoly quantity). If firm 2
were to choose the quantity corresponding to perfect competition, such
that , then firm 1’s optimum would be to produce nil: . This is the
point at which marginal cost intercepts the marginal revenue corresponding to .

3.  .
It can be shown that, given the linear demand and constant marginal cost, the function is also linear. Because we have
two points, we can draw the entire function , see diagram 3. Note the axis of the graphs has changed, The
function is firm 1’s reaction function, it gives firm 1’s optimal choice for each possible choice by firm 2. In other
words, it gives firm 1’s choice given what it believes firm 2 is doing
The last stage in finding the Cournot equilibrium is to find firm 2’s reaction function. In this case it is symmetrical to firm 1’s as
they have the same cost function. The equilibrium is the intersection point of the reaction curves.